1. Hero Section (Main Visual & Tagline)
Yamagishi Complexity Torus Lab | Yuki Yamagishi Laboratory
— Small Lab, Infinite Structure. —
Exploring the Hidden Structures of a Torus‑Shaped Universe.
“From a geometric perspective, we clarify the mathematical structures underlying established physical laws.”
The Yamagishi Complexity Torus Lab is a private research laboratory led by independent researcher Yuki Yamagishi. Our work focuses on geometric decoding of physical theories, grounded in the solid‑angle quantity $4\pi$ and the n=2 Uniqueness Theorem. We investigate geometric structures appearing in mechanics, electromagnetism, quantum theory, and relativity, aiming to reformulate them through precise geometric interpretation.
2. Research Overview — What We Research
Research Focus: Geometric Decoding of the “$n=2$ Uniqueness Theorem” and the “Cosmic OS”
Rather than proposing new physical laws or rewriting existing theories, our laboratory pursues a structural approach:
“Making the geometric meaning of known laws visible and correctly interpretable.”
The $n=2$ Uniqueness Theorem & Solid Angle $4\pi$
We demonstrate and formalize the mathematical mechanism by which only $n=2$ yields uniform mass‑increase rates in spherically symmetric density distributions in 3D space, and how the limiting mass $m = 4\pi$ (the full solid angle) naturally emerges.
Cosmic OS (Information‑Geometric Model)
We reinterpret the universe as an information‑rendering system—a Cosmic Operating System—and restructure classical mechanics, quantum mechanics, electromagnetism, and gravitational theory using shared geometric quantities ($4\pi$, $16\pi^2$, etc.) and information‑processing metrics such as latency and geometric cost.
Multifaceted Verification of Geometric & Topological Structures
We explore structural stability of the universe through multiple routes: information‑geometric reformulations of the Poincaré Conjecture, loop‑geometry measures ($16\pi^2$), dimensional hierarchy models, potential theory, and information theory.
3. Publications & Preprints
Extensive Open‑Access Papers Available on Zenodo
Our research outputs are published on Zenodo, an international open‑access repository. Each paper provides rigorous algebraic verification and geometric reinterpretation of established physical and mathematical theories.
Paper 01: The $n=2$ Uniqueness Theorem in Spherical Density Distributions
A four‑route proof (geometry, mechanics, potential theory, information theory) establishing the necessity of $n=2$ and the emergence of $m = 4\pi$.
Paper 02: The $4\pi$ Mass‑Cancellation Theorem
Formalizing the appearance of pure solid angle in inverse‑square fields and the structure of frictionless equilibrium.
Papers 07 & 08: Information‑Geometric Reformulation of the 3D/4D Poincaré Conjecture
Density‑structural interpretations based on Perelman’s Ricci flow and Hopf fibration.
Papers 12–16: Einstein–Yamagishi Volume‑Restoration Equation & Total‑Synchronization Equation
Analysis of geometric equivalence among $E = mc^2 = 4\pi c^2$, Coulomb’s law, and gravitational fields.
Papers 44, 46/47, 50: Dimensional Hierarchy Unification & Loop‑Geometry Measure Theory
Reduction of Planck quantities via $c^N/(4\pi)^\varepsilon$, geometric identity of $16\pi^2$ in quantum field theory, and decomposition of the Planck‑pressure limit.
4. Academic Integrity — The Independent Researcher’s Stance
Rigorous Self‑Verification and Continuous Revision (2nd & 3rd Editions)
As an independent researcher, the most important principle is “rigorous self‑verification and logical precision.”
Even after releasing first editions of papers, we continually re‑examine assumptions and derivations. If circular reasoning or missing premises are discovered, claims are promptly revised or withdrawn, and updated editions (2nd, 3rd) are published.
We avoid overstating discoveries or claiming resolution of unsolved problems.
Our work remains strictly within the domain of geometric interpretation of established theories.
Errors and limitations are openly disclosed, ensuring reproducibility and academic reliability.
This transparent revision process forms the foundation of our research integrity.
5. Contact & Language Support
For inquiries, discussions, or feedback regarding our research, please reach out via the Contact Us page.
We support communication in multiple languages.